Lemma 2.2 [1]} [2]}
We have \(\zeta (s) = O_{\delta }(|t|^{\frac{1-\sigma }{3}+\delta })\)  uniformly for \(|t|\ge 2\)  and \(1/2 \le \sigma \le 1\) . For \(\sigma \ge 1-c(\log t)^{-2/3}\) , \(\zeta (s) \ll (\log |t|)^{2/3}\)  for \(|t| \ge 2\) . For \(\sigma > 1\) , \(\zeta (s) \ll 1/(\sigma -1)\) .

